Existence of the solutions and the attractors for the large-scale atmospheric equations

作     者：HUANG Haiyang1 & GUO Boling2 1. Department of Mathematics, Beijing Normal University, Beijing 100875, China 2. Institute of Applied Physics and Computational Mathematics, Beijing 100080, China 

作者机构：1. Department of Mathematics Beijing Normal University Beijing 100875 China 2. Institute of Applied Physics and Computational Mathematics Beijing 100080 China 

出 版 物：《Science China Earth Sciences》 (中国科学（地球科学英文版）)

年 卷 期：2006年第49卷第6期

页      面：650-660页

核心收录：

学科分类：07[理学] 070601[理学-气象学] 0706[理学-大气科学] 

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.10371011 and 90511009) 

主　　题：atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium. 

摘      要：In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.